the si system of measurement. the nature of measurement part 1 - number part 2 - scale (unit)...

The SI System of Measurement

The Nature of Measurement

Part 1 - numberPart 2 - scale (unit)

Examples:20 grams

6.63 x 10-34 Joule·seconds

A Measurement is a quantitative observation consisting of TWO parts

The Fundamental SI Units (le Système International, SI)

Physical Quantity Name Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Electric Current Ampere A

Amount of Substance mole mol

Luminous I ntensity candela cd

SI Base UnitsA base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units. Examples:1 Kg = The Legrand K

1 sec. = radiation frequency of a cesium-133 atom1 meter = distance light travels in 1/299,792,458th of a second.

SI Base Units

The SI base unit for temperature is the kelvin.• Most often confused with Celsius.

At zero kelvin, there exist virtually no particle motion or kinetic energy. This temperature is known as absolute zero.

SI Base Units

A unit that is defined by a combination of base units is called a derived unit.• Volume is a derived unit. Volume is

calculated by multiplying (length x width x volume).Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).

• Density is a derived unit, g/cm3, the amount of mass per unit volume. Density is calculated by dividing (mass/volume)

SI PrefixesCommon to Chemistry

Prefix Unit Abbr. ExponentKilo k 103

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

Metric ConversionsgmL 10-1 10-2 10-3101102103

Baseunit

deci centi millidekahectokilo

Conversions in the metric system are merely a matter of moving a decimal point. The “base unit” means the you have a quantity (grams, meters, Liters, etc without a prefix.


Baseunit


Example #1: Convert 18 liters to milliliters

18 L1 2 3

18 liters = 18 000 milliliters


Baseunit


Example #2: Convert 450 milligrams to grams

123450 mg450 mg = 0.450 g


Baseunit


Example #3: Convert 20 kilograms to milligrams

20 kg1 2 3 4 5 6

20 kg = 20 000 000 mg

Uncertainty and Significant Figures

Cartoon courtesy of Lab-initio.com

Uncertainty in Measurement

A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Why Is there Uncertainty? Measurements are performed with instruments

No instrument can read to an infinite number of decimal places

Which of these balances has the greatest uncertainty in measurement?

Precision and AccuracyAccuracy refers to the agreement of a particular value with the true value.

Precision refers to the degree of agreement among several measurements made in the same manner.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Rules for Counting Significant Figures - DetailsNonzero integers always count as significant figures.

3456 has 4 significant figures

Rules for Counting Significant Figures - Details

Zeros- Leading zeros do not count as

significant figures.

0.0486 has3 significant figures


Zeros- Captive zeros

always count assignificant figures.



ZerosTrailing zeros are significant only if the number contains a decimal point.



Exact numbers have an infinite number of significant figures.

1 inch = 2.54 cm, exactly

Sig Fig Practice #1How many significant figures in each of the following?

1.0070 m 5 sig figs

17.10 kg 4 sig figs

100,890 L 5 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 2 sig figs

Rules for Significant Figures in Mathematical Operations

Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.

6.38 x 2.0 =12.76 13 (2 sig figs)

Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures in Mathematical Operations

Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement.

6.8 + 11.934 =18.734 18.7 (3 sig figs)

Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Scientific Notation

In science, we deal with some very LARGE numbers:

1 mole = 602000000000000000000000

In science, we deal with some very SMALL numbers:

Mass of an electron =0.000000000000000000000000000000091 kg

Scientific Notation

Imagine the difficulty of calculating the mass of 1 mole of electrons!

0.000000000000000000000000000000091 kg x 602000000000000000000000

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Scientific Notation:A method of representing very large

or very small numbers in the form:

M x 10n

M is a number between 1 and 10

n is an integer

2 500 000 000

Step #1: Insert an understood decimal point

.

Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal point

123456789

Step #4: Re-write in the form M x 10n

2.5 x 109

The exponent is the number of places we moved the decimal.

0.0000579

Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal pointStep #4: Re-write in the form M x 10n

1 2 3 4 5

5.79 x 10-5

The exponent is negative because the number we started with was less than 1.

PERFORMING CALCULATIONS IN SCIENTIFIC

NOTATION

ADDITION AND SUBTRACTION

Review:Scientific notation expresses a number in the form: M x 10n

1 M 10n is an integer

4 x 106

+ 3 x 106

IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.

7 x 106

4 x 106

- 3 x 106

The same holds true for subtraction in scientific notation.

1 x 106

4 x 106

+ 3 x 105

If the exponents are NOT the same, we must move a decimal to make them the same.

4.00 x 106

+ 3.00 x 105 + .30 x 106

4.30 x 106Move the decimal on the smaller number!

4.00 x 106

A Problem for you… 2.37 x 10-6

+ 3.48 x 10-4

2.37 x 10-6

+ 3.48 x 10-4

Solution…002.37 x 10-

6

+ 3.48 x 10-4

Solution…0.0237 x 10-4

3.5037 x 10-4

Metric Conversion

Practice

Problem #1Convert 400 mL to Liters

400 mL= L

mL

L

1 000

1 .400

= 0.4 L

= 4x10-1 L

Problem #2Convert 10 meters to mm

10 m= m

mm

mm

1

1 000 10 000

= 1x104 mm

Problem #3Convert 73 grams to kg

73 g= kg

g

kg

1 000

1 0.073

= 7.3x10-2 kg

Problem #4Convert 0.02 kilometers to m

0.02 km= m

km

m

1

1 000 20

= 2x101 m

Problem #5Convert 20 centimeters to m

20 cm= m

cm

m

100

1 0.20

= 2x10-1 m

Problem #6Convert 450 milliliters to dL

450 mL= dL

mL

dL

100

1 4.5

Problem #7Convert 10 kilograms to grams

10 kg= g

kg

g

1

1 000 10 000

= 1x104 g

Problem #8Convert 935 mg to cg

935 mg= cg

mg

cg

10

193.5

= 9.35x101 cg

Problem #9Convert 5.2 kg to mg

5.2 kg= m

gkg

mg1

1 000 000

= 5 200 000 mg= 5.2x106 mg

Problem #10Convert 175 mL to cm3

175 mL= cm3

mL

cm3

1

1175

= 1.75x102 cm3

Representing Data: Graphs

A graph is a visual display of data that makes trends easier to see than in a table.

Parts of A Graph

Title

X- Axis : Independent VariableY- Axis: Dependent Variable

Description of variables

Types of Graphs

There are 3 main types of graphs that are used in science.1. Bar Graph2. Pie Chart/ Circle Graph3. Line Graph

Bar Graph

A bar graph is a visual display used to compare the amounts or frequency of occurrence of different characteristics of data. • This type of display allows us to: compare

groups of data, and. to make generalizations about the data quickly.

Pie Chart/ Circle Graph

A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

Line Graph

A line graph is useful for displaying data or information that changes continuously over time. Another name for a line graph is a line chart. • This is typically the most popular in

science.

Graph Interpretation

1. What is this graph about?2. At what age to teens have

the most cell phones?3. At what age do teens have

the least amount of cell phones?

4. How many cell phones do 15 yr. olds have?

5. How many cell phones do 16.5 yr. olds have?

6. What is the greatest number of cell phones at any age?

7. What is the lowest number of cell phones at any age?

Graph Interpretation

1. How many sectors does this graph have?

2. What percentage of people preferred chocolate Ice Cream?

3. If 50 people were surveyed how many people preferred Vanilla?

the si system of measurement. the nature of measurement part 1 - number part 2 - scale (unit)...

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si system of measurement